I'm trying to upload and/or embed some audio files into my blog, hosted on Google's Blogspot, but cannot seem to do so. The three audio files, about 2.5 hours of recording, total about 35MB in size of all the files.

How can I embed them in my blog where I can also make it available for listening and download?

Attempts:

SoundCloud - they have a limit on "tape" and allow only two hours of free upload. I exceeded that.

OurMedia - it never uploaded even when it said it did.

Mediafire - only allows people to download, and not everyone will care to do so - some may only want to listen to it online and leave.

I'm also trying to have it show up on the blog with "music player interface" so people can play it straight from my blog itself and download it if they want.

Answer to your question is no you can't host audio on blogger servers, earlier they allowed it when FTP blogs were allowed, but now only video upload is available, which some use for hosting audio using a smaller truncated youtube player!

there are two things:
a. host audio;
b. host audio player;

You can use combinations that fit you in security, privacy and convenience

Host your audio someplace safe (means public access to the file remains at least as long as the service remains) such as amazon 5 GB, Google Music and use audio player from Google to embed it.

Update: Amazon's cloud drive doesn't offer public links.

Host your audio on services which offer their own players soundcloud which has 2 hour limit on uploads, my favorites: divshare 2 gb (no time based limits) and spreaker which offers 20 hours storage! there are countless others.

Use external hosts like dropbox, google drive, box for both player and audio, use google audio player.

You can host mp3 in Google drive, change permissions to read-only to anyone with link, it is not a direct link but it is to preview the file, you can download the file and then immediately cancel it, copy the download link in your downloads tab, remove the session id or timeout variables after the (?), use the link with the embed code by Leo!